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Chapter 14: Problem 162

For solutions of the same concentration, as acid strength increases, indicate what happens to each of the following (increases, decreases, or doesn't change). a. \(\left[\mathrm{H}^{+}\right]\) d. \(\mathrm{pOH}\) b. \(\mathrm{pH}\) e. \(K_{\mathrm{a}}\) c. \(\left[\mathrm{OH}^{-}\right]\)

Short Answer

Expert verified
As the acid strength increases for solutions of the same concentration, the following changes occur: a. \([\mathrm{H}^{+}]\) increases b. pH decreases c. \([\mathrm{OH}^{-}]\) decreases d. pOH increases e. \(K_{\mathrm{a}}\) increases

Step by step solution

01

Effect on \([\mathrm{H}^{+}]\) and \(K_{\mathrm{a}}\)

As the acid strength increases, it will dissociate in solution to a greater extent. This means that there will be a higher concentration of hydrogen ions (\([\mathrm{H}^{+}]\)) in the solution. Since \(K_{\mathrm{a}}\) represents the acid dissociation constant, a higher \(K_{\mathrm{a}}\) value indicates that the acid is stronger. Therefore, as the acid strength increases the \(K_{\mathrm{a}}\) value also increases.
02

Effect on pH

The pH of a solution is a measure of the concentration of hydrogen ions (\([\mathrm{H}^{+}]\)) in the solution and is given by the formula: pH = \(-\log_{10}[\mathrm{H}^{+}]\) As we determined in the previous step, the concentration of hydrogen ions (\([\mathrm{H}^{+}]\)) in the solution increases as the acid strength increases. According to the pH formula, when \([\mathrm{H}^{+}]\) increases, the pH value will decrease. Therefore, as the acid strength increases, the pH decreases.
03

Effect on \([\mathrm{OH}^{-}]\) and pOH

The relationship between hydrogen ion concentration (\([\mathrm{H}^{+}]\)) and hydroxide ion concentration (\([\mathrm{OH}^{-}]\)) in a solution is given by the ion product constant of water, \(K_{w}\): \(K_{w} = [\mathrm{H}^{+}][\mathrm{OH}^{-}]\) where \(K_{w}\) is constant at a given temperature (e.g., \(1 \times 10^{-14}\) at 25°C). As \([\mathrm{H}^{+}]\) increases due to the increase in acid strength, the concentration of hydroxide ions \([\mathrm{OH}^{-}]\) must decrease to maintain the constant value of \(K_{w}\). Therefore, as the acid strength increases, the \([\mathrm{OH}^{-}]\) decreases. Similarly, pOH is a measure of the concentration of hydroxide ions and is given by the formula: pOH = \(-\log_{10}[\mathrm{OH}^{-}]\) As \([\mathrm{OH}^{-}]\) decreases, the pOH value will increase. Therefore, as the acid strength increases, the pOH increases. To summarize: a. Concentration of hydrogen ions (\([\mathrm{H}^{+}]\)) increases b. pH decreases c. Concentration of hydroxide ions (\([\mathrm{OH}^{-}]\)) decreases d. pOH increases e. Acid dissociation constant (\(K_{\mathrm{a}}\)) increases

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Acid Dissociation Constant
Understanding the acid dissociation constant, often represented as \(K_{a}\), is essential to grasp why some acids are stronger than others. In chemistry, the strength of an acid is a measure of its ability to donate \(H^{+}\) ions when in solution. The \(K_{a}\) value quantifies this ability, revealing the degree to which an acid dissociates into its ions. When we have two solutions of the same molarity, the one with a higher \(K_{a}\) indicates a stronger acid, as it is more fully dissociated into \(H^{+}\) and its conjugate base. This directly conveys that more \(H^{+}\) ions are present in the solution, leading to a lower pH.

As acidity increases, \(K_{a}\) increases, because more \(H^{+}\) ions are available in the solution. It’s a reflection of an acid's eagerness to part with its \(H^{+}\) ion and is a critical part of understanding acid behavior in both theoretical and practical applications. This concept is at the core of a variety of chemical processes, such as buffer systems in biological contexts and acid-base reactions in industrial settings.
pH and pOH Relationship
The pH scale is a convenient way to express the acidity or basicity of a solution. It is inversely related to the concentration of hydrogen ions (\(H^{+}\)), meaning that as the \(H^{+}\) concentration increases, the pH decreases indicating more acidity.

pH Calculation

The pH is calculated using the negative logarithm of the \(H^{+}\) ion concentration, while the pOH represents the acidity of the hydroxide ions (\(OH^{-}\)) and follows a similar logarithmic scale.

The pH and pOH scales are interrelated by the equation \(pH + pOH = 14\) at 25°C, which is derived from the ion product constant for water (\(K_{w}\)). A lower pH means a higher acid concentration, while a low pOH indicates higher alkalinity. This relationship helps us analyze chemical solutions' acidity and alkalinity without directly measuring ion concentrations, making it a foundational concept in chemistry for numerous applications.
Concentration of Hydrogen Ions
The concentration of hydrogen ions \(\left[\mathrm{H}^{+}\right]\) plays a pivotal role in defining the acidity of a solution. Simply put, the more \(H^{+}\) ions present, the more acidic the solution is. In a stronger acid, these ions break away more willingly from their parent molecule, increasing the \(\left[\mathrm{H}^{+}\right]\) in the solution.

Acidity Impact

The impact on acidity is immediate and quantifiable: a high concentration of these ions results in a lower pH value and indicates a more acidic environment. This concept is crucial for predicting the behavior of acids in different conditions, which is valuable not only in academic settings but also in commercial industrial processes where acid concentration affects reaction outcomes.
Hydroxide Ion Concentration
Understanding hydroxide ion concentration \(\left[\mathrm{OH}^{-}\right]\) is vital when discussing the basicity of solutions. When an acid dissociates, it increases the \(H^{+}\) concentration, but this also has an inverse effect on \(\left[\mathrm{OH}^{-}\right]\) due to the self-ionization equilibrium of water. At a constant temperature, as the \(H^{+}\) ions increase in solution, the \(\left[\mathrm{OH}^{-}\right]\) must decrease to maintain the equilibrium characterized by water’s ion product constant (\(K_{w}\)).

The reduction in \(\left[\mathrm{OH}^{-}\right]\) leads to an increase in pOH, which measures the basicity of a solution on a logarithmic scale, similar to pH but for basic substances. This relationship is essential for various applications, such as balancing chemical equations and designing titration experiments in lab settings.

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Most popular questions from this chapter

Aluminum hydroxide is an amphoteric substance. It can act as either a Brønsted-Lowry base or a Lewis acid. Write a reaction showing \(\mathrm{Al}(\mathrm{OH})_{3}\) acting as a base toward \(\mathrm{H}^{+}\) and as an acid toward \(\mathrm{OH}^{-}\).

Are solutions of the following salts acidic, basic, or neutral? For those that are not neutral, write balanced equations for the reactions causing the solution to be acidic or basic. The relevant \(K_{\mathrm{a}}\) and \(K_{\mathrm{b}}\) values are found in Tables \(14.2\) and \(14.3\). a. \(\mathrm{Sr}\left(\mathrm{NO}_{3}\right)_{2}\) c. \(\mathrm{CH}_{3} \mathrm{NH}_{3} \mathrm{Cl}\) e. \(\mathrm{NH}_{4} \mathrm{~F}\) b. \(\mathrm{NH}_{4} \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) d. \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{NH}_{3} \mathrm{ClO}_{2}\) f. \(\mathrm{CH}_{3} \mathrm{NH}_{3} \mathrm{CN}\)

The equilibrium constant \(K_{\mathrm{a}}\) for the reaction \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons{\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5}(\mathrm{OH})^{2+}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q)}\) is \(6.0 \times 10^{-3}\). a. Calculate the \(\mathrm{pH}\) of a \(0.10-M\) solution of \(\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}^{3+}\). b. Will a \(1.0-M\) solution of iron(II) nitrate have a higher or lower \(\mathrm{pH}\) than a \(1.0-M\) solution of iron(III) nitrate? Explain.

Write out the stepwise \(K_{\mathrm{a}}\) reactions for the diprotic acid \(\mathrm{H}_{2} \mathrm{SO}_{3}\)

Consider a \(0.67-M\) solution of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\left(K_{\mathrm{b}}=5.6 \times 10^{-4}\right)\). a. Which of the following are major species in the solution? i. \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}\) ii. \(\mathrm{H}^{+}\) iii. \(\mathrm{OH}^{-}\) iv. \(\mathrm{H}_{2} \mathrm{O}\) v. \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{3}{ }^{+}\) b. Calculate the \(\mathrm{pH}\) of this solution.
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